Coupled System

exercise 3_1200

\((a)\) Find the general solution to \(\frac{d\vec{u}}{dt}=A\vec{u}\) if :

\(A = \begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \end{bmatrix}\)

\((b)\) Find a time \(T\) at which the solution \(\vec{u}(T)\) is guaranteed to return to the initial value \(\vec{u}(0)\). (Hint: use Euler's formula, \(e^{ix}=cos(x)+isin(x)\))